An astronaut in a really well climate controlled space suit...

An Astronaut (in a REALLY well climate-controlled space suit) experiences gravitational fields of different strengths in the following locations. Rank the locations in order of increasing gravitational field strength.

Transcript

00:01 Hello everyone so let's start with the question as you can see in the diagram there are three locations that is a b and each has different set of gravitational condition the relative planet mass and relative distance of each location from the planet's center are shown okay, so here are the three planets and here there are mass and the distance between them.

00:22 Okay, so here suppose say distance between the center of the planet to the center point is what to are here from point? point b to center of this planet there is red planet is 3r and from point c to 2 this planet blue is distance is 2r and there is mass also mentioned okay so we have to find means we have to find what the gravitational strength okay that is field strain we have to find the rankings and we have to explain the condition of this field strength okay so i am solving the solution so here first we have to find what we have to show the work done to start to some solve the gravitational strength means in g terms and m and r okay so as we know that our gravitational strength our gravitational strength is proportional proportional to mass and inversely proportional square of the distance if i want to write in equation form i can write it down in this way that is our g equal to what g m by r square so this is our gravitational field strength so here our planet for point a our g a equal to g a equal to what g that is our gravitational constant point five m divided by two are the whole square okay in means you can see in the diagram that uh from point eight to to the planet the distance is what 2 r and the mass of this planet is 0 .5m so putting this value in this equation okay so our answer will be what gm by 8 r square similarly for planet for point b i can write g b equal to g 3m divided by 3 r the whole square after solving this our answer will be what gm m 3 are the point c that is our gravitational field strength will be what g multiply by 2m divided by 2 r the whole square and our answer will be what gm by 2r square okay as you can see from the equation that g is inversely proportional to r okay so as the value of g decreases our gravitational free strength increases and as the value of our gravitational field strength decreases using this concept i can solve the second question is that what we have to do we have to show the ranking so as per this concept i can write it down that our point c is greater than point b which is greater than point a okay so this is the ranking is the ranking of points a b and c so this is the concept except for this for the ranking now in third as i can explain that means if we have to find the what condition would make for the largest field strength so i can write it down more the mass more the mass less the distance and from the planet from the planet center would make would make largest g like as the mass of means increase increases, as the mass of the planet increases, the distance between them will be like less.

04:31 So that concept will make the planet largest...

Question

An Astronaut (in a REALLY well climate-controlled space suit) experiences gravitational fields of different strengths in the following locations. Rank the locations in order of increasing gravitational field strength.

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